Spectral analysis is a well-known analytical tool, which has been used for decades in science and industry to characterize materials, processes and systems based on spectral information. For example, cross-correlation of spectral data provides amplitude and phase information between two signals, which have some common component generated by some common artificial or natural process. In radio astronomy, cross-correlation allows very weak signals from distant astronomical sources to be extracted from strong independent system noise. Amplitude and phase from many different antennae are then used to build an image of the radio source. In network analysis an artificial signal is generated, transmitted through an object under test, and is then cross-correlated with the original signal. This yields the amplitude and phase response as a function of frequency of the tested object. In aperture synthesis radar an object is irradiated by a high power microwave source. Cross-spectral analysis of the microwave reflections from the object's surface is used to produce an image of the object. Auto-correlation of a signal is used in spectrum analysis to find periodic signal components in signals disturbed by random noise. Another field for the application of spectral analysis is in phased array systems such as phased array radar, remote sensing phased array receivers and wide-band phased antennae.
In most of these applications it is desired to use real time digital signal processing to determine the spectrum of a sampled analog signal. Known signal processing systems use mixed analog and digital systems. Furthermore, in current phased array systems analog methods for sub-sample delay interpolation are used. However, analog systems are inherently unstable due to time and temperature variability of analog filters.
Therefore, real time digital processing systems using time-domain de-multiplexing have been recently developed. Unfortunately, these systems require more than an order of magnitude more digital hardware for large array systems than a direct method, as noted below. Furthermore, these systems are often limited by clock rates of the digital equipment that are much lower than the bandwidths of signals to be processed. It is desirable to use digital techniques in real time to determine the spectrum of a sampled analog signal whose bandwidth exceeds the capability of realized digital systems to obtain the spectrum directly. A direct method according to the prior art would require digital processing to occur at clock rates of twice the bandwidth of the signal.
Recent developments in computer technology overcome the limitations of processor clock rates by processing one task on a plurality of processors in parallel in order to process a large amount of data processed in a fraction of the time needed by a one-processor system.
It is, therefore, an object of the invention to provide a method and system based on parallel processing techniques to determine a wide-band spectrum efficiently with arbitrarily high spectral resolution using a processor clock rate that is an arbitrary fraction of the wide-band clock rate.
It is another object of the invention to provide a precision sub-sample digital delay interpolation for phased array and cross-correlation systems.